Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 14 - Section 14.4 - Tangent Planes and Linear Approximation - 14.4 Exercise - Page 935: 27



Work Step by Step

Given: $m=p^{5}q^{3}$ The differential form can be evaluated as follows: $dw=\dfrac{\partial w}{\partial x} dx + \dfrac{\partial w}{\partial y} dy $ We need to find the partial derivatives w.r.t. $p$ and $q$ as follows: $dm= \dfrac{\partial m}{\partial p}dp+\dfrac{\partial m}{\partial q}dq$ Here, we get $ \dfrac{\partial m}{\partial p}dp=(5) p^{4}q^{3}dp$ and $\dfrac{\partial m}{\partial q}dq=(3) p^{5}q^{2}dq$ Hence, we have $dm=5p^{4}q^{3}dp+3p^{5}q^{2}dq$
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